Evaluating residual stress in structural components is a critical concern in civil engineering, particularly for ensuring the safety and integrity of infrastructure. Accurate stress assessment in essential load-bearing components is challenging due to restricted accessibility and complex boundary conditions. Resonance-based vibration methods offer a non-destructive approach for stress evaluation, but their effectiveness is often limited in situ by the uncertainty of boundary conditions. In recent years, alternative non-destructive evaluation (NDE) techniques such as ultrasonics have gained traction for structural health monitoring. Among these, the acoustoelastic technique based on nonlinear acoustics has shown promise in assessing structural stress states. In this study, experimental and numerical investigations were conducted to evaluate both the resonance-based vibration method and the acoustoelastic method. Both techniques were applied to a uniaxially stressed steel plate at various load levels. Their accuracy in evaluating the actual stress was then compared. The results demonstrate that the acoustoelastic method provides reliable stress measurements without requiring detailed knowledge of boundary conditions, highlighting its potential as a practical alternative to vibration-based methods for field applications.